The epikarst, a zone of increased weathering near the land surface, determines the distribution of recharge to a karst aquifer in both space and time. It links climatic and near-surface geological conditions with the karstification of a limestone aquifer, defining both the hydraulic and the chemical boundary conditions for the development of the karst system. Realistic modeling of the epikarst is therefore a prerequisite for the simulation of karst aquifer genesis. A conceptual model of the joint karst-epikarst evolution is presented in this paper. An epikarst module is developed and implemented in a numerical continuum--discrete conduit flow model for karst genesis, which accounts for the joint evolution of the epikarst and the main karstic conduit network under unconfined conditions. The influence of epikarst genesis on the evolution of the underlying karst aquifer is investigated in four scenarios. It is found that only the interaction of epikarst and initial heterogeneity in the underlying carbonate rock leads to the development of a dendritic cave system. If no heterogeneity in the initial conduit network or in the recharge distribution is included, maze-type caves develop.